We describe in detail the stochastic multi-step game corresponding to the European option pricing problem on an incomplete market with discrete time and a finite number of assets, without transaction costs and trading restrictions. Recurrent Bellman-type relations for the upper and lower guaranteed values of the game are given. The equivalence of the following statements is established: the market model is arbitrage-free; there are option seller's portfolios delivering minimum in the Bellman-type relations; there is a super-hedging portfolio for the European option. The game with an arbitrage-free market model results in an equilibrium. Based on this statement, we propose to construct a super-hedging portfolio via a seller's game strategy. Examples of analytical European option pricing on an incomplete market with a finite support and numerical pricing of an option for gold are given.